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While going through some questions on chirality and optical isomerism, I came across this compound:

Compound

Note that I have marked 3 carbons as $C_1,C_2,C_3$

Its obvious that $C_1,C_3$ are chiral carbons.

$C_2$ is not a chiral carbon as it has the same group above and below it( With respect to the picture)

However a thought struck me that chiral carbon meant that 4 different groups are attached to it.

But what exactly does same group mean?

Does it mean that even the spatial arrangement of the groups should be different?

Or does it not matter?

So if spatial arrangement mattered, then the compound I have mentioned would have a chiral $C_2$ carbon for specific configurations around $C_1$ and $C_3$ carbons.

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  • $\begingroup$ C1 and C3 are chiral atoms, and are of the variety R or S. As a consequence, RR and SS are optically active. But the combinations RS and SR are optically inactive. They are meso compounds. $\endgroup$
    – Maurice
    Jun 21, 2020 at 19:30
  • $\begingroup$ Even in the meso compound, C2 is pseudochiral. $\endgroup$
    – Zhe
    Jun 21, 2020 at 22:02
  • $\begingroup$ C2 is achirotopic but stereogenic with a configuration of r (lower case). $\endgroup$
    – user55119
    Jun 21, 2020 at 22:47

2 Answers 2

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Yes, spatial configuration of attached groups matters. Meaning different stereo configuration of $C_1$ and $C_3$ may render $C_2$ either chiral or not:

enter image description here

Also because you have more than 1 stereo center you're not limited to just enantiomers, you can get diastereomers - the molecules will be different even though they're not mirror images of each other:

enter image description here

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The compound must pass the sigma test, as in symmetry. If you imagine a mirror cross sectioning the molecule with more than one chiral carbon and the substituents of the chiral centers are cis, then the molecule is achiral. If the substituents are in a trans configuration, then the molecule is chiral.

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  • $\begingroup$ Don't we use R and S for this instead of cis and trans? Thanks for the answer anyway! $\endgroup$ Jun 22, 2020 at 19:33
  • $\begingroup$ R and S are to designate what direction the substituents of the enantiomers rotate in respect to the chiral center. Cis and Trans are used for denoting whether a compound with two or more chiral centers is chiral or not. $\endgroup$ Jun 22, 2020 at 19:37

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